At the top level of your zappajs instance definition, right alongside where you define your @use statements, define routes/templates, and so on, you can call into the @io object, which is a reference into the socket.io server-side instance. You just put:
@io.set 'log level', 1
@io.set('log level', 1)
Log level 1 is the least chatty of them all. You can see the different levels to choose the one you want here.